Pointing MX and Autodiscover to 365

You may go ahead with the MX cutover and Autodiscover change to Exchange Online without any issues. This will eliminate your Dependency on Exchange On-premises and Hybrid to some extent. Hope you have the Defender for Office 365 License.  Also, please make sure to create the Defender for Office365 Policies, Anti-phishing policy, Antispam policy, Antimalware policy, SafeLink attachment policy, and SafeLink Policy. There won't be any issues for you with the On-premises resource mailbox functionalities by doing these changes. By the way, is there any reason to keep the resource mailboxes On-premises? You may migrate them to the cloud to remove the complete dependency on the on-premises server and Exchange Hybrid.

Not sure how your room booking works. With autodiscover pointing to EXO, Outlook clients of EXO based mailboxes would not be able to connect to the on-prem mailboxes. You might be able to configure Outlook on those devices to force a connection to on-premises Exchange. Otherwise you could migrate the mailboxes and configure the room booking app to connect to EXO mailboxes. There's hardly any room booking systems that don't support EXO mailboxes.

I can't think of any impact of changing mail flow by pointing MX record at EXO as long as you are syncing all AD objects to Entra ID

Curious_Kevin16​ 

If you have an Exchange Server on-premises in a hybrid configuration, you can use Basic auth to authenticate with the Exchange Server on-premises or configure the Exchange Server on-premises with a Receive connector that Allow anonymous relay on Exchange servers.

Exchange Online to retire Basic auth for Client Submission (SMTP AUTH)